FINITE GROUPS WITH SOME SEMI-p-COVER-AVOIDING OR ss-QUASINORMAL SUBGROUPS
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초록
Suppose that G is a finite group and H is a subgroup of G. H is said to be an ss-quasinormal subgroup of G if there is a subgroup B of G such that G = HB and H permutes with every Sylow subgroup of B; H is said to be semi-p-cover-avoiding in G if there is a chief series 1 = G0 < G1 < · · · < Gt = G of G such that, for every i = 1, 2, . . . , t, if Gi/Gi−1 is a p-chief factor, then H either covers or avoids Gi/Gi−1. We give the structure of a finite group G in which some subgroups of G with prime-power order are either semi-p-cover-avoiding or ss-quasinormal in G. Some known results are generalized.
Abstract
Suppose that G is a finite group and H is a subgroup of G. H is said to be an ss-quasinormal subgroup of G if there is a subgroup B of G such that G = HB and H permutes with every Sylow subgroup of B; H is said to be semi-p-cover-avoiding in G if there is a chief series 1 = G0 < G1 < · · · < Gt = G of G such that, for every i = 1, 2, . . . , t, if Gi/Gi−1 is a p-chief factor, then H either covers or avoids Gi/Gi−1. We give the structure of a finite group G in which some subgroups of G with prime-power order are either semi-p-cover-avoiding or ss-quasinormal in G. Some known results are generalized.
참고문헌 (8)
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